TY - CHAP A1 - Giersch, Thomas A1 - Beirow, Bernd A1 - Popig, Frederik A1 - Kühhorn, Arnold T1 - FSI-based forced response analyses of a mistuned high pressure compressor blisk T2 - 10th International Conference on Vibrations in Rotating Machinery, 11-13 September 2012, IMechE London, UK KW - Mistuning KW - Blisk KW - Aeroelastics Y1 - 2012 SN - 978-0-85709-452-0 SN - 0-85709-452-1 N1 - Paper C1326/012 PB - Woodhead Publ. CY - Cambridge, UK ER - TY - GEN A1 - Beirow, Bernd A1 - Golze, Mark A1 - Popig, Frederik T1 - Vibration Reduction of a Steam Turbine Wheel by Means of Intentional Mistuning T2 - Advances in Mechanism Design III : Proceedings of TMM 2020 N2 - A last stage steam turbine wheel is analyzed with the objective to alleviate the flutter susceptibility by employing intentional mistuning (IM). In particular, the operation at nominal speed under part-load conditions may cause unfavorable flow conditions facilitating flow separation. In consequence, negative aerodynamic damping ratios occur for the first bending mode family in some circumstances. Employing intended alternate mistuning of adequate magnitude has proved to be a promising measure to stabilize rotors in terms of avoiding self-excited vibration phenomena. From the manufacturing point of view, this two-blade design is advantageous as well and hence, chosen here as a first measure to attenuate flutter susceptibility. Two prototypes of bladed disks series have been made, which are exhibiting small but unavoidable deviations from the design intention due to manufacturing. The real blade alone frequencies have been identified within foregoing experimental investigations. Numerical modal analyses carried out for the prototypes as manufactured finally reveal that there is an additional positive contribution of random mistuning in terms of further enhancing the least aerodynamic damping ratio. Another promising and robust IM pattern is found by using generic algorithms to optimize the least aerodynamic damping ratio yielding stable conditions at any time as well. Moreover, it shows that IM combined with random mistuning also mitigates the maximum forced response at part-speed conditions. KW - Intentional mistuning KW - Blade vibration KW - Flutter KW - Forced response KW - Optimization KW - Aeroelastics Y1 - 2022 SN - 978-3-030-83593-4 SN - 978-3-030-83594-1 U6 - https://doi.org/10.1007/978-3-030-83594-1_8 SN - 2211-0984 SN - 2211-0992 SP - 73 EP - 82 PB - Springer CY - Cham ER - TY - CHAP A1 - Popig, Frederik A1 - Hönisch, Peter A1 - Kühhorn, Arnold T1 - Experimental and Numerical Analysis of Geometrical Induced Mistuning T2 - ASME Turbo Expo 2015: Turbine Technical Conference and Exposition Volume 7B: Structures and Dynamics Montreal, Quebec, Canada, June 15–19, 2015 N2 - The application of high pressure compressor (HPC) rotors manufactured as blisk (Blade Integrated Disk) is ever-expanding in modern jet engine designs. Despite the major advantages of less mass and higher efficiency, the most challenging problem is lower mechanical damping due to the loss of damping between blades root’s and the disk. Mistuning is induced by material inhomogeneities, manufacturing tolerances or wear during use and leads to amplitude magnification and mode localization. From the experimental point of view mistuning can be evaluated via experimental vibration analysis in terms of frequency deviations. Furthermore optical measurements can be evaluated in terms of geometrical deviations between the real and designed geometry. From the structural point of view a mistuned blisk model can be obtained by morphing the nodes of the geometrical tuned FE model or by performing blade individual stiffness mistuning due to modification of Young’s modulus. The following work is focused on the numerical prediction of mistuned blisk vibrations. Therefore, the research blisk of the 4 stage research compressor, manufactured as job-production, is analyzed. For this research blisk optical measurement data as well as experimentally obtained frequency patterns are available. In a first part mistuning identification in terms of experimental vibration analysis and Proper Orthogonal Decomposition of the geometrical deviations is presented. In a second part mistuning modeling in terms of stiffness mistuning and geometrical mistuning is applied to the tuned FE-model and the numerical results are evaluated against experimental data regarding accuracy. Furthermore, the impact of geometrical deviations on mistuning is analyzed. Copyright © 2015 by Rolls-Royce Deutschland Ltd & Co KG KW - Numerical analysis KW - Blades KW - Finite element model KW - Disks KW - Stiffness KW - Damping Y1 - 2015 UR - http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleID=2428632 SN - 978-0-7918-5677-2 U6 - https://doi.org/10.1115/GT2015-43272 PB - ASME CY - New York, NY ER - TY - GEN A1 - Beirow, Bernd A1 - Kühhorn, Arnold A1 - Weber, Robby A1 - Popig, Frederik T1 - Vibration Analyses of an Axial Turbine Wheel with Intentional Mistuning T2 - Journal of Engineering for Gas Turbines and Power N2 - The last stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes unfavorable flow conditions may occur which increases the risk of flutter at part load conditions. For this reason, intentional mistuning is employed with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits. In this sense, two different series of blades have been made. However, small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since centrifugal stiffening effects significantly attenuate the blade-to-blade frequency difference. Focusing on the first flap mode it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed evokes an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Finally, mistuning patterns could be identified featuring a tremendous increase of aerodynamic damping ratios. The robustness of the solutions could be proved by superimposing additional random mistuning. KW - Blades KW - Computer simulation KW - Damping KW - Design KW - Disks KW - Flow (Dynamics) KW - Flutter (Aerodynamics) KW - Vibration analysis Y1 - 2021 U6 - https://doi.org/10.1115/1.4049449 SN - 1528-8919 SN - 0742-4795 VL - 143 IS - 6 ER - TY - GEN A1 - Beirow, Bernd A1 - Golze, Mark A1 - Popig, Frederik T1 - Application of Intentional Mistuning to Reduce the Vibration Susceptibility of a Steam Turbine Wheel T2 - ASME 2022 Turbomachinery Technical Conference & Exposition (GT2022) N2 - Intentional mistuning (IM) is employed on a last stage turbine wheel to alleviate both the flutter susceptibility and maximum forced response. Primarily, operations at nominal speed under part-load conditions may cause unfavorable flow conditions facilitating flow separation. As a consequence, the original design intention with identical blades features negative aerodynamic damping ratios with respect to the first bending mode family. In order to prevent any self-excited vibration phenomena, intentional alternate mistuning is utilized to increase the least aerodynamic damping ratio as far as it takes a positive value and hence, to contribute to a stabilization of the rotor. For the purpose of numerically analyzing the vibration behavior, reduced order models are built up, which are based on modal reduction techniques, namely the subset of nominal system modes (SNM) [1] and the fundamental mistuning model (FMM) [2]. These types of models conveniently allow for considering both, different mistuning distributions in terms of probabilistic analyses and the aeroelastic interaction by means of prescribing aerodynamic damping ratios and aeroelastic natural frequencies of the tuned counterpart or aerodynamic influence coefficients, respectively. A detailed study is presented regarding the correction of frequency mistuning magnitudes in terms of considering the impact of centrifugal stiffening, which plays a significant role in case of long low pressure turbine blades featuring high aspect ratios. Since alternate IM cannot be implemented perfectly, every bladed wheel as manufactured will exhibit small but unavoidable structural deviations from the design intention, which are known as random mistuning. To ensure the robustness of the IM solution in terms of positive aerodynamic damping ratios at any time, comprehensive probabilistic analyses are conducted with respect to superimposing random structural mistuning at first. Secondly, the impact of varying mistuning magnitude is analyzed. Thirdly, the robustness towards aerodynamic mistuning is investigated by means of small variations of aeroelastic influence coefficients and consequently, the inter blade phase angle dependent aerodynamic damping curves. Moreover, it becomes apparent that alternate IM superimposed with both, random structural and aerodynamic mistuning also mitigates the maximum forced response at part-speed conditions. Y1 - 2022 UR - https://asme-turboexpo.secure-platform.com/a/solicitations/167/sessiongallery/10144/application/82208 ER - TY - CHAP A1 - Beirow, Bernd A1 - Golze, Mark A1 - Popig, Frederik ED - Beran, Jaroslav ED - Bílek, Martin ED - Václavík, Miroslav ED - Žabka, Petr T1 - Vibration Reduction of a Steam Turbine Wheel by Means of Intentional Mistuning T2 - Advances in Mechanism Design III N2 - A last stage steam turbine wheel is analyzed with the objective to alleviate the flutter susceptibility by employing intentional mistuning (IM). In particular, the operation at nominal speed under part-load conditions may cause unfavorable flow conditions facilitating flow separation. In consequence, negative aerodynamic damping ratios occur for the first bending mode family in some circumstances. Employing intended alternate mistuning of adequate magnitude has proved to be a promising measure to stabilize rotors in terms of avoiding self-excited vibration phenomena. From the manufacturing point of view, this two-blade design is advantageous as well and hence, chosen here as a first measure to attenuate flutter susceptibility. Two prototypes of bladed disks series have been made, which are exhibiting small but unavoidable deviations from the design intention due to manufacturing. The real blade alone frequencies have been identified within foregoing experimental investigations. Numerical modal analyses carried out for the prototypes as manufactured finally reveal that there is an additional positive contribution of random mistuning in terms of further enhancing the least aerodynamic damping ratio. Another promising and robust IM pattern is found by using generic algorithms to optimize the least aerodynamic damping ratio yielding stable conditions at any time as well. Moreover, it shows that IM combined with random mistuning also mitigates the maximum forced response at part-speed conditions. KW - steam turbine KW - vibration KW - intentional mistuning Y1 - 2022 SN - 978-3-030-83593-4 SN - 978-3-030-83596-5 U6 - https://doi.org/10.1007/978-3-030-83594-1_8 SN - 2211-0984 SN - 2211-0992 SP - 73 EP - 82 PB - Springer International Publishing CY - Heidelberg ER - TY - GEN A1 - Beirow, Bernd A1 - Kühhorn, Arnold A1 - Weber, Robby A1 - Popig, Frederik T1 - Vibration Analyses of an Axial Turbine Wheel With Intentional Mistuning T2 - Turbo Expo 2020, Virtual Conference, Virtual Conference and Exhibition, Online, September 21 – 25, 2020 N2 - The last stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes unfavorable flow conditions may occur which can lead to flow separation in some circumstances. Consequently, there is the risk of flutter in principle, particularly at nominal speed under part load conditions. For this reason, intentional mistuning is employed by the manufacturer with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits since only two different blade designs are allowed. In this sense, two different series of blades have been made. However, it is well known that small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional but unwanted deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since it significantly attenuates the blade to blade frequency difference in this particular case. Within an academic study the turbine wheel is modelled as blade integrated disk in order to demonstrate fundamental effects of intentional mistuning on flutter susceptibility and forced response. For that purpose, reduced order models are built up by using the subset of nominal system mode approach introduced by Yang and Griffin [1], which conveniently allows for taking into account both differing mistuning patterns and the impact of aeroelastic interaction. Focusing on the first flap mode it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed affects an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Again only two different blade designs are admitted. Finally, mistuning patterns could be identified causing a tremendous increase of aerodynamic damping ratios. The robustness of the solutions found could be proved by superimposing additional random mistuning. Another study is focused on the impact of mistuning strength. Further analyses are addressing the forced response at part speed conditions, where different resonance crossings are becoming apparent in the Campbell plot. An increase of the forced response compared to the tuned counterpart is partly unpreventable because of unfavorable aerodynamic damping curves. Independently, the maximum forced response has to be limited also in case of applying large intentional mistuning. [1] Yang, M. T., Griffin, J. H., „A Reduced-Order model of Mistuning Using a Subset of Nominal System Modes“. J Eng Gas Turb Power, 123, pp. 893-900 (2001). Y1 - 2020 UR - https://asme-turboexpo.secure-platform.com/a/solicitations/105/sessiongallery/5325/application/45830 ER -